100ed10: Difference between revisions

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The '''100 equal divisions of the 10th harmonic''' is a nonoctave tuning of about 39.8631 steps each. It corresponds to 30.102999 EDO, the first digits of the decimal logarithm of 2. It can be thought of as [[30edo]], but with [[10/1]] instead of 2/1 ~~being just~~.

The '''100 equal divisions of the 10th harmonic''' is a nonoctave tuning of about 39.8631 steps each. It corresponds to 30.102999 EDO, the first digits of the decimal logarithm of 2. It can be thought of as [[30edo]], but with [[10/1]] being just instead of [[Octave|2/1]].

100ed10 can be labeled as a "Homo sapiens tunning", by analogy of how [[27edt|27ed3]] is labeled "Klingon tuning".

== Theory ==

The step error of any given harmonic in 100ed10 can be simply extracted through 3rd and 4th base digits of the decimal logarithm.

100ed10 is suitable for use with the 2.5.11.17 subgroup, a significant departure from it simply being "30edo with stretched octaves".

100ed10 contains a unique coincidence - it is contorted order-10 in the 2.5 subgroup, which makes up the number 10. In the 2.3.5, it is contorted order-2. While in the 7-limit it no longer has contorsion, the individual harmonics still do derive from smaller ED10s - 2.7 subgroup is contorted order-5. 100ed10 is suitable for use with the 2.5.11.17 subgroup, a significant departure from it simply being "30edo with stretched octaves", and it is suitable with the following commas:

~~100ed10 bears a base~~-~~10 coincidence aggregate. It's approximates of 2nd and 5th harmonics~~, ~~which multiply to 10~~, ~~are steps 30 and 70~~, ~~which themselves derive form 10ed10.~~

* [7, -3, 0, 0⟩ (128/125)

* [0, -5, 1, 2⟩ (3179/3125)

* [7, 2, -1, -2⟩ (3200/3179)

* [-1, -2, 4, -2⟩ (14641/14450)

* [14, -1, -1, -2⟩ (16384/15895)

* [8, -1, -4, 2⟩ (73984/73205)

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-The '''100 equal divisions of the 10th harmonic''' is a nonoctave tuning of about 39.8631 steps each. It corresponds to 30.102999 EDO, the first digits of the decimal logarithm of 2. It can be thought of as [[30edo]], but with [[10/1]] instead of 2/1 being just.
+{{Infobox ET}}
+The '''100 equal divisions of the 10th harmonic''' is a nonoctave tuning of about 39.8631 steps each. It corresponds to 30.102999 EDO, the first digits of the decimal logarithm of 2. It can be thought of as [[30edo]], but with [[10/1]] being just instead of [[Octave|2/1]].
 ed10 can be labeled as a "Homo sapiens tunning", by analogy of how [[27edt|27ed3]] is labeled "Klingon tuning".
 == Theory ==
-{{primes in edo|edo=30.103}}
+{{Harmonics in equal|100|10|columns=10}}
 The step error of any given harmonic in 100ed10 can be simply extracted through 3rd and 4th base digits of the decimal logarithm.
-ed10 is suitable for use with the 2.5.11.17 subgroup, a significant departure from it simply being "30edo with stretched octaves".
+ed10 contains a unique coincidence - it is contorted order-10 in the 2.5 subgroup, which makes up the number 10. In the 2.3.5, it is contorted order-2. While in the 7-limit it no longer has contorsion, the individual harmonics still do derive from smaller ED10s - 2.7 subgroup is contorted order-5. 100ed10 is suitable for use with the 2.5.11.17 subgroup, a significant departure from it simply being "30edo with stretched octaves", and it is suitable with the following commas:
-ed10 bears a base-10 coincidence aggregate. It's approximates of 2nd and 5th harmonics, which multiply to 10, are steps 30 and 70, which themselves derive form 10ed10.
+* [7, -3, 0, 0⟩ (128/125)
+* [0, -5, 1, 2⟩ (3179/3125)
+* [7, 2, -1, -2⟩ (3200/3179)
+* [-1, -2, 4, -2⟩ (14641/14450)
+* [14, -1, -1, -2⟩ (16384/15895)
+* [8, -1, -4, 2⟩ (73984/73205)